What will be the sign of the product if we together multiply $199$ negative integers and $10$ positive integers?

The correct option is A Negative
Multiplication of $2$ negative integer result into positive integer.

If we multiply $199$ negative integer, then the result will be negative integer

Now if we multiply $10$ positive numbers with $199$ negative integers

we will get a negative integer because multiplication of negative and positive

integer will always result in negative integer.

Hence option A is correct.